I've been trying to get the hang of AJE, and I think I must be missing a key point of the battle mechanics. Namely, I can't ever seem to get a decisive victory! Whenever I fight a battle I more or less trade even on losses, win the battle, and push the enemy back. Then I push him back again. And again... In some of the more limited scenarios I've been able to literally just hound an enemy army and after probably 10-12 battles I destroy or near-destroy their stack. But I'd like to find a more efficient way of doing things.

I've tried a lot of different scenarios, and never have much luck. In the Rome vs Senones scenario I chase the Gauls endlessly through Northern Italy, never losing a battle but never quite winning the war either. In the Year of Four Emperors I chase the Jews around Judaea, inflicting big defeats on their main stack until he does something like retreat over the Dead Sea where I take 50 days to follow him.

I just don't understand what else I should be doing. Surely there's some way to completely shatter enemy stacks without having to just chase them endlessly! What am I missing?

Hard to give you specific advice as its all a bit situational - and depends a bit on what you have to hand.

At the end of a battle, cavalry are a real force mulitpiier, not much use with the Romans in the early scenarios but helps in the later games. In effect if you win, and have cavalry, you will inflict a lot more hits.

Numbers count, while the combat routine makes the enemy more likely to try and pull back if badly outnumbered, every now and then they will stand, at that stage raw numbers can really convert a small to a big win.

Ranged fire helps - again less for the Romans in the BoR scenarios, but this will disrupt before combat making any melee victories easier and more dangerous.

Operationally, try to take some MC in the likely retreat province. A small force of cavalry or light infantry in the red-green stance can close off retreat routes or at least dictate the region of retreat. This is very useful in BoR due to the small scale

If you attack, try not to do so with low cohesion. Even if you win you'll find your forces break off early.

Leadership traits can all come into play, some commanders have traits that build on the concepts above such as more troops/frontage, pursuit, speed (ie less cohesion loss as you move) etc.

Your opponent matters. If you are fighting mostly light troops in poor terrain they will tend to escape. Think of it as less of a stand up fight with formed battlelines and more a running skirmish. Welcome to the realistic AGEOD problem of how to deal with irregulars/rebels and poor terrain. In the games time frame this explains why the Jewish revolt lasted so long and why the conquest of Spain was over centuries. Boxing them in by getting control of the wider region is your best strategy.

loki100's advice is very sound. So I merely add a few other thoughts. In all AGEOD games you must readjust to the reality of historical games. Very few battles in any age were decisive. In most, the opponent managed to get away with a mostly intact army. Thus, an incremental approach to defeating your enemy is needed. I always think of the generals in the American Civil War who sought the one great battle to win the war none of whom could actually achieve this feat.

I think of needing to gradually gain National Morale until the point where your army has the morale and leadership to quickly defeat an opponent. But in most AJE games you win with patience and craft, rarely with one grand blow.